Question

A cereal company believes more than 1.5% of their packages are too damaged to sell. A random study of 100 boxes finds that 2 are damaged to this point. In this study, the test statistic is Z=. and the observed significance of the test is?

Answer 1

In this hypothesis test problem, we are testing whether the proportion of damaged packages is greater than 1.5%. We can use the normal distribution to perform the test by calculating the test statistic Z and comparing it to the critical value. If Z is greater than the critical value, we reject the null hypothesis.

Step-by-step explanation:

The given problem is a hypothesis test problem where we are testing whether the proportion of damaged packages is greater than 1.5%. We can use the normal distribution to perform the hypothesis test. The test statistic Z is calculated by subtracting the hypothesized proportion (1.5%) from the observed proportion (2 damaged boxes out of 100) and dividing by the standard error.

Z = (p - P) / √(P(1-P)/n)

We can then compare the test statistic Z to the critical value to determine the observed significance of the test. If Z is greater than the critical value, we reject the null hypothesis.